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Power series for the secans
The secans can be expressed as the power series
Explanation
The first derivative of the secans is
Only the secans and the tangent are used. If we determine further derivatives this will remain the same, because (tan x)' = sec2x, so
The point x = 0 gives sec (0) = 1 and tan (0) = 0 so
We substitute this in the Taylor series and find
General format
You can write the power series as a sum
where Un is the n-th up/down number. Or
where E2n is the n-th Euler number.